Algebra/Quadratic Equation

The solutions to the general-form quadratic function ax2+bx+c=0{\displaystyle ax^{2}+bx+c=0} can be given by a simple equation called the quadratic equation. To solve this equation, recall the completed square form of the quadratic equation derived in the previous section:

The part under the radical sign, b2−4ac{\displaystyle {b^{2}-4ac}} , is called the discriminant, Δ{\displaystyle \Delta } . The value of the discriminant tells us some useful information about the roots.

If Δ>0{\displaystyle \Delta >0} , there are two unique real solutions.

If Δ=0{\displaystyle \Delta =0} , there is one unique real solution.

If Δ<0{\displaystyle \Delta <0} , there are two unique, conjugate imaginary solutions.

If Δ{\displaystyle \Delta } is a perfect square then the two solutions are rational, otherwise they are irrational conjugates.